I can't say I know of any switches on the water heater.
As far as wiring going to the the WH, if you open the outside door on the WH compartment you will be able to tell there if it has electrical wires coming to it or not. Mine are very visible.
If you have the SCHWINTEK IN-WALL SLIDE system, they have been a big problem for everyone who has them. Some say they just have to be "reset" synchronized, others had to have the motors replaced, and the list goes on.
The hinge problem--in my opinion, they will have to replace the entire hinge to fix the problem.
On the heat problem, have you pulled the floor register off and looked in there with a mirror and flashlight? Some times the run is disconnected or hasn't been connected, and sometimes the "end" of the run hasn't been closed off and all the heat is being forced into the under belly.
If that particular floor register is coming directly from/off the furnace, trace it back to where it hooks on to the furnace and see if it's connected, plus check to make sure the plates are all in place and haven't fallen off. You might want to use some aluminum furnace tape on some of this stuff to ensure it stays on and to seal any leaks,